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Saturday, January 3, 2009

Thresholding for Edge Detection

The real world is noisy, and the differencing operations of edge detection tend to magnify that noise. We can apply some statistical methods to our edge detection to hopefully overcome that. A very basic approach is to threshold based on a histogram of the gradient magnitude. Taking a look at the distribution of gradient magnitude for our trusty old electricity meter (shown below), it looks like a pixel level below about 235 puts us safely out into the tail of the distribution. Most pixels (in this image) are not edge pixels, so they are clustered on the high end of the scale.
This is pretty easy to do with numpy and Image (PIL):

Of course the histogram shape will depend on how much noise and how many edges are in the particular picture. This one had black dials on a white background, and not much noise so thresholding is a pretty fruitful strategy for really pulling out the edges.
You can make an intuitive argument that gradient magnitude distributions will have roughly similar shapes to that shown above. Especially as image resolutions steadily increase, the vast majority of pixels will not be on an edge. Sort of the curse of dimensionality in reverse, I guess that makes it a blessing.